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1.
We propose new formulas for singular vectors in Verma modules over the affine Lie superalgebra
. We analyze the coexistence of singular vectors of different types and identify the twisted modules arising as submodules and quotient modules of
Verma modules. We show that with the twists (spectral flow transformations) properly taken into account, a resolution of irreducible representations can be constructed consisting of only the
modules. 相似文献
2.
A. M. Semikhatov 《Theoretical and Mathematical Physics》1997,112(2):949-987
We review several constructions that are realized in bosonic and N = 2 strings and which relate the affine Lie algebra
(2), affine superalgebra
(2|1), and the superconformal N = 2 algebra.
This paper was written at the request of the Editorial Board.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 112, No. 2, pp. 195–240, August, 1997. 相似文献
3.
S. E. Klevtsov 《Theoretical and Mathematical Physics》2008,154(2):201-208
We describe a construction of the quantum-deformed affine algebras using vertex operators in the free field theory. We prove
the Serre relations for the Borel subalgebras of quantum affine algebras; in particular, we consider the
case in detail. We also construct the generators corresponding to the positive roots of
.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 2, pp. 240–248, February, 2008. 相似文献
4.
B. Enriquez 《Theoretical and Mathematical Physics》1994,98(3):256-258
We note that a version with spectral parameter of the Drinfeld-Sokolov reduction gives a natural mapping from the KdV phase space to the group of loops with values in
: affine nilpotent andA principal commutative (or anisotropic Cartan) subgroup; this mapping is connected to the conserved densities of the hierarchy. We compute the Feigin-Frenkel action of
(defined in terms of screening operators) on the conserved densities in thesl
2 case.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 98, No. 3, pp. 375–378, March, 1994. 相似文献
5.
G. L. Rybnikov 《Journal of Mathematical Sciences》1992,59(5):1117-1123
Generators of the space of tensor invariants of the Lie algebra Sl2([t]) are constructed. It is proved that the restrictions of a spinor representation of the affine Lie algebra
to
and
form a dual pair. A realization of the fundamental representations of the Lie algebra
is obtained.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Akad. Nauk SSSR, Vol. 172, pp. 137–144, 1989. 相似文献
6.
D. R. Lebedev S. Z. Pakuliak S. M. Khoroshkin 《Theoretical and Mathematical Physics》1997,110(1):18-34
The representation theory of centrally extended Yangian doubles is investigated. The intertwining operators are constructed
for infinite dimensional representations of
, which are deformed analogs of the highest weight representations of the affine algebra
at level 1. We give bosonized expressions for the intertwining operators and verify that they generate an algebra isomorphic
to the Zamolodchikov-Faddeev algebra for the SU(2)-invariant Thirring model. From them, we compose L-operators by Miki’s method
and verify that they coincide with L-operators constructed from the universal R-matrix. The matrix elements of the product
of these operators are calculated explicitly and are shown to satisfy the quantum (deformed) Knizhnik-Zamolodchikov equation
associated with the universal R-matrix for
.
This paper was written at the request of the Editorial Board.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 110, No. 1, pp. 25–45. January, 1997. 相似文献
7.
A renormalization group transformation R
1 has a single stable point
in the space of the analytic circle homeomorphisms with a single cubic critical point and with the rotation number
(the golden mean). Let a homeomorphism T be the C
1-conjugate of
. We let
denote the sequence of distribution functions of the time of the kth entrance to the nth renormalization interval for the homeomorphism T. We prove that for any
, the sequence
has a finite limiting distribution function
, which is continuous in
, and singular on the interval [0,1]. We also study the sequence
for k>1. 相似文献
8.
V. P. Maslov 《Theoretical and Mathematical Physics》2002,131(2):666-680
We consider the Gibbs statistical ensemble. We introduce the statistical-weight operator
, construct the entropy operator
of the ensemble using the Boltzmann formula
, and define the free-energy operator. We find asymptotic expressions for free-energy eigenvalues with pair correlations taken into account in the limit as the number of systems in the ensemble tends to infinity. 相似文献
9.
In the examples of the N=2 super-Virasoro algebra and the affine
algebra, we investigate the construction of unitary representations of infinite-dimensional algebras in terms of collective excitations over a filled Dirac sea of fermionic or bosonic operators satisfying a generalized exclusion principle and represented by semi-infinite forms in the modes of one of the generators. We develop the methods for investigating properties of semi-infinite spaces (polynomial realization of the dual space) and for constructing the appropriate algebra action on these spaces (a filtration by subspaces similar to Demazure modules). We also consider relations of the semi-infinite realizations to the Rogers–Ramanujan-type identities, to the expression of coinvariants through meromorphic functions on products of Riemann surfaces with a prescribed behavior on multiple diagonals, and to some combinatorial facts; we also consider the relation between modular functors and fusion rules for the N=2 and
theories. 相似文献
10.
Johannes Schoissengeier 《Monatshefte für Mathematik》1992,114(2):139-147
A proof of the formula
for locally compact fields
andC
1-isomorphisms :UV, whereU andV are open subsets of
, was never published. In this paper we give two short proofs, one of them is a more elementary variant of the other. 相似文献
11.
S. Pakuliak 《Theoretical and Mathematical Physics》1995,104(1):810-822
Some relations between different objects associated with quantum affine algebras are reviewed. It is shown that the Frenkel-Jing bosonization of a new realization of the quantum affine algebra
as well as bosonization of L-operators for this algebra can be obtained from Zamolodchikov-Faddeev algebras defined by the quantum R-matrix satisfying unitarity and crossing-symmetry conditions.On leave of absence from the ITP, Kiev 252143, Ukraine. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 104, No. 1, pp. 64–77, July, 1995. 相似文献
12.
V. D. Lyakhovsky 《Theoretical and Mathematical Physics》2006,148(1):968-979
In accordance with the quantum duality principle, the twisted algebra
is equivalent to the quantum group
and has two preferred bases: one inherited from the universal enveloping algebra
and the other generated by coordinate functions of the dual Lie group
. We show howthe transformation
can be explicitly obtained for any simple Lie algebra and a factorable chain
of extended Jordanian twists. In the algebra
, we introduce a natural vector grading
, compatible with the adjoint representation of the algebra. Passing to the dual-group coordinates allows essentially simplifying
the costructure of the deformed Hopf algebra
, considered as a quantum group
. The transformation
can be used to construct new solutions of the twist equations. We construct a parameterized family of extended Jordanian
deformations
and study it in terms of
; we find new realizations of the parabolic twist.
Dedicated to the birthday of my teacher, Yurii Novozhilov
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 148, No. 1, pp. 112–125, July, 2006. 相似文献
13.
V. Ostrik 《Transformation Groups》1997,2(3):279-287
We study the tensor category
of tilting modules over a quantum groupU
q
with divided powers. The setX
+ of dominant weights is a union of closed alcoves
numbered by the elementswW
f
of a certain subset of affine Weyl groupW. G. Lusztig and N. Xi defined a partition ofW
f
into canonical right cells and the right order
R
on the set of cells. For a cellAW
f
we consider a full subcategory
formed by direct sums of tilting modulesQ() with highest weights
. We prove that
is a tensor ideal in
, generalizing H. Andersen's theorem about the ideal of negligible modules which in our notations is nothing else then
. The proof is an application of a recent result by W. Soergel who has computed the characters of tilting modules.This material is based upon work supported by the U.S. Civilian Research and Development Foundation under Award No. RM1-265. 相似文献
14.
We show that the TQ equation is satisfied by the trace over the quantum space of the product of R-matrices intertwining two representations of the quantum double of the Borel subalgebra of the affine algebra
(the standard two-dimensional and the N-dimensional cyclic representations). 相似文献
15.
Yasmine B. Sanderson 《Journal of Algebraic Combinatorics》2000,11(3):269-275
We show that the specialization of nonsymmetric Macdonald polynomials at t = 0 are, up to multiplication by a simple factor, characters of Demazure modules for
. This connection furnishes Lie-theoretic proofs of the nonnegativity and monotonicity of Kostka polynomials. 相似文献
16.
We give a uniform interpretation of the classical continuous Chebyshev and Hahn orthogonal polynomials of a discrete variable
in terms of the Feigin Lie algebra
for λ∈ℂ. The Chebyshev and Hahn q-polynomials admit a similar interpretation, and orthogonal polynomials corresponding to
Lie superalgebras can be introduced. We also describe quasi-finite modules over
, real forms of this algebra, and the unitarity conditions for quasi-finite modules. Analogues of tensors over
are also introduced.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 123, No. 2, pp. 205–236, May, 2000. 相似文献
17.
V. M. Badkov 《Mathematical Notes》1973,13(5):453-459
For the polynomials {pn(t)}
0
, orthonormalized on [–1, 1] with weightp(t) = (1–t) (1+t)
v=1
m
, we obtain necessary and sufficient conditions for boundedness of the sequences of norms: 1)
2)
and 3)
with the conditions that
on [–1, 1] and (H,)–1 L2(0, 2), where(H,) is the modulus of continuity in C(–1, 1) of function H.Translated from Matematicheskie Zametki, Vol. 13, No. 5, pp. 759–770, May, 1973. 相似文献
18.
Takuya Hara 《Integral Equations and Operator Theory》1992,15(4):551-567
Let
be a Hilbert space. A continuous positive operatorT on
uniquely determines a Hilbert space
which is continuously imbedded in
and for which
with the canonical imbedding
. A Kreîn space version of this result, however, is not valid in general. This paper provides a necessary and sufficient condition for that a continuous selfadjoint operatorT uniquely determines a Kreîn space (
) which is continuously imbedded in
and for which
with the canonical imbedding
. 相似文献
19.
Ton Daorong 《数学学报(英文版)》1990,6(1):47-56
In this paper we discuss the completions (,
) of a commutativel-groupG with respect to the intrinsic topologies . We give some conditions under which
is the intrinsic topology of the same type on as
and give the relations between these completions. 相似文献
20.
Ganikhodzhaev N. N. Mukhamedov F. M. Rozikov U. A. 《Theoretical and Mathematical Physics》2002,130(3):425-431
We consider the Potts model on the set in the field Q
p of p-adic numbers. The range of the spin variables (n),
, in this model is
. We show that there are some values q=q(p) for which phase transitions occur. 相似文献